Bring the eggs to room temperature by leaving them out of refrigerator for a couple hours.
In the meantime, prepare the sauce base by adding the rest of the ingredients to a medium pot. Bring the mixture to a boil, and the turn the heat down to a simmer. Cover and simmer for 10 minutes. Then turn off the heat, open the lid, set it aside, and let it cool completely.
Bring another pot of water to a boil for the eggs. Once boiling, gently and quickly lower the eggs into the boiling water using a large spoon. You want to avoid dropping them and cracking them on the bottom of the pot. Let the eggs cook in the boiling water for 7 minutes (it’s a good idea to set a timer). Once the timer goes off, turn off the heat, quickly scoop out the eggs, and transfer to an ice bath. Allow them to sit in the ice bath until they are completely cool to the touch. The purpose here is to stop cooking the eggs any further.
Once the eggs are cooled, lightly crack the egg shells. The goal here is to make enough cracks to allow the flavor of the sauce base to seep into the egg. I like to use a small spoon to tap the eggs, but be careful! It you tap or crack too hard, you might crack open the egg since the egg yolk is still very soft.
Soak the cracked eggs in your sauce base for 24 hours in the refrigerator, making sure all the eggs are completely submerged in the sauce base. After 24 hours, they’re ready! You can also soak them longer for a stronger flavor. These eggs last for 3 to 4 days in the refrigerator.